Polylactic acid (PLA) is a bio-based, biodegradable polymer that presents high potential for biomedical and sensing applications. Ongoing works reported in the literature concern mainly applications based on 3D printing, while textile applications are hindered by the limited flexibility of PLA and its composite filaments. In the present work, PLA/multiwall carbon nanotube (MWCNT) composite filaments were produced with enhanced flexibility and electrical conductivity, which may be applied on a textile structure. A biodegradable plasticizer was incorporated in the nanocomposites, aiming at improving MWCNT dispersion and increasing the flexibility of the filaments. Filaments were produced with a range of compositions and their morphology was characterized as well as their thermal, thermomechanical, and electrical properties. Selected compositions were tested for sensing activity using saturated acetone vapor, demonstrating a suitable response and potential for the application in fabrics with sensing capacity.